Since the \(B_c^\ast \)  or \(B_c(1^3 S_1)\)  state has not been observed yet,
we will use the value \(m(B_c^\ast )~=~6331(4)(6)\)  MeV obtained from
lattice QCD [1]}. The values of size parameters
are taken from our previous papers [2]}, [3]}, [4]}. Their numerical values are given in Table REF .
<TABLE>